Development of study of nonlinear system as applied analysis
| Project/Area Number |
20540141
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Waseda University |
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Principal Investigator |
NISHIDA Takaaki Waseda University, 理工学術院, 教授 (70026110)
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| Research Collaborator |
TERAMOTO Yoshiaki 摂南大学, 工学部, 教授 (40237011)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 応用数学 / 非線形偏微分方程式系 / 力学系 / 熱対流問題、 / パターン形成 / 解空間大域構造 / 計算機援用解析 / 計算機援用証明法 / 熱対流問題 |
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| Research Abstract |
Main objects are Dynamical Systems, Nonlinear Hyperbolic Conservation Laws and Fluid Dynamical Equations. After considering the pattern formations and the structure of solutions we proceed to study their global structure of the solution spaces such as bifurcation diagrams and their stability by analysis and computer assisted analysis. Global bifurcation diagrams for Rayleigh-Benard heat convection problems, bifurcation theorems for Benard-Marangoni heat convection problems and a constructive existence theorem by a finite difference method for the Hamilton-Jacobi equation corresponding to a special Hamiltonian with two degree of freedom are obtained.
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Report
(4 results)
Research Products
(22 results)
